http://www.tandem-associates.c...onel/lionelident.htm For postwar transformer options look there. For modern options, try the venders in the ad banner on the top of the page. They pay for ads so this site can remain free, help um out so they can continue.
That set looks great! Likely not a thing wrong. It doesn't look run much at all really.
If the cord seems fine, and you want to use the original transformer, plug it into a power strip that has a built in cicuit breaker. The lower the breaker amps the better at first power up. A switched strip is better yet. If you'll notice there isn't a zero volt setting. All done? Just shut the strip down till next time.
Add a circuit breaker and/or 4-5 amp fuse between track and transformer too, if there is not one built onto the transformer. A new one in addition to anything there sure wont hurt, and would ensure disconnection should time have froze up the internal one. Early ones didn't always have a breaker (it would be a button on the top. But fyi, a button could be a whistle/horn too,. Can we see the top please?) An automotive fuse or breaker will do. If you use fuses, buy extra. There are vintage add on breakers that usually function well also.
It won't matter which wire goes to which side of the lock-on at this point. Just start at the low volt "steps" and see if you need a higher voltage or not.
Oil it before you run it! Oil all axles and pivots. Oil or a dot of grease on rub areas.
Make sure the bushings , and gear post get it good. Also where the gear rests on the frame and spins. If you can work grease into that frame/gear gap, that works too. I would lay it on its side, oil it, spin the wheels some and let gravity do its thing for an hour, then flip and repeat. Then let it sit upright on a rag to allow excess to drip off the wheels(overnight), then wipe the wheels well. Oily wheel treads aren't good for traction.
Any rust, oil and wait for rust to soak some then agitate with a brass brush, wipe clean, repeat. Doing this repeatedly, over time the rust will vanish. (The tender body rust needs a different approach)
The motor shaft needs some too, but go extremely light, a tiny drop only, for the brush plate's side so it just wets the shaft some, but doesn't wet the armature plate and brushes (OK if oil gets there, but it tends to collect brush dust, eventually gunking up the plate gaps, then you have to clean. When dry, the dust tends to fly off) Finally a dab of grease on the gears teeth till they are greased.
Any power supply 75w or more will do the trick. In fact, it can even run on DC volts. (Whistle tenders need AC volts, the loco won't be picky) I will suggest if you use a modern one to make sure it has pure sine wave output. Some things in the world of model trains insist on it. 75w is usually good for a small-medium track size (40'-ish total).
In my opinion its far better to buy more power than you really need, than finding out you need more later. You just don't hear, "darn I bought too big a transformer", unless they are speaking about the footprint or height.
ZW is Lionel's Best, any era.
Fantastic set to get started with! The transformer "looks" OK but it's hard to tell from just a photo. As long as the cord flexes easily and there are no cracks or flaking it should be safe. If in doubt take it to a hobby shop and ask if someone there can look it over for you. BTW, welcome aboard! 
